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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[Sebastian Raschka](http://www.sebastianraschka.com)  \n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import time\n",
      "print('Last updated: %s' %time.strftime('%d/%m/%Y'))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Last updated: 10/06/2014\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<hr>\n",
      "I would be happy to hear your comments and suggestions.  \n",
      "Please feel free to drop me a note via\n",
      "[twitter](https://twitter.com/rasbt), [email](mailto:bluewoodtree@gmail.com), or [google+](https://plus.google.com/118404394130788869227).\n",
      "<hr>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Linear regression via the least squares fit method"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a name=\"sections\"></a>\n",
      "<br>\n",
      "<br>\n"
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Sections"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "- [Introduction](#Introduction)\n",
      "\n",
      "- [Least squares fit implementations](#Least-squares-fit-implementations)\n",
      "\n",
      "    - [The matrix approach in Python and NumPy](#The-matrix-approach-in-Python-and-NumPy)\n",
      "    \n",
      "    - [The classic approach in Python](#The-classic-approach-in-Python)\n",
      "    \n",
      "- [Visualization](#Visualization)\n",
      "\n",
      "- [Performance growth rates](#Performance-growth-rates)\n",
      "\n",
      "- [Results](#Results)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a name=\"introduction\"></a>\n",
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Introduction"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[[back to top](#Sections)]"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Linear regression via the least squares method is the simplest approach to performing a regression analysis of a dependent and a explanatory variable. The objective is to find the best-fitting straight line through a set of points that minimizes the sum of the squared offsets from the line.  \n",
      "The offsets come in 2 different flavors: perpendicular and vertical - with respect to the line.  \n",
      "![](https://raw.githubusercontent.com/rasbt/python_reference/master/Images/least_squares_vertical.png)  \n",
      "![](https://raw.githubusercontent.com/rasbt/python_reference/master/Images/least_squares_perpendicular.png)  \n",
      "\n",
      "As Michael Burger summarizes it nicely in his article \"[Problems of Linear Least Square Regression - And Approaches to Handle Them](http://www.arsa-conf.com/archive/?vid=1&aid=2&kid=60101-220)\": \"the perpendicular offset method delivers a more precise result but is are more complicated to handle. Therefore normally the vertical offsets are used.\"  \n",
      "Here, we will also use the method of computing the vertical offsets.\n",
      "\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In more mathematical terms, our goal is to compute the best fit to *n* points $(x_i, y_i)$ with $i=1,2,...n,$ via linear equation of the form  \n",
      "$f(x) = a\\cdot x + b$.  \n",
      "We further have to assume that the y-component is  functionally dependent on the x-component.  \n",
      "In a cartesian coordinate system, $b$ is the intercept of the straight line with the y-axis, and $a$ is the slope of this line."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In order to obtain the parameters for the linear regression line for a set of multiple points, we can re-write the problem as matrix equation  \n",
      "$\\pmb X \\; \\pmb a = \\pmb y$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\Rightarrow\\Bigg[ \\begin{array}{cc}\n",
      "x_1 & 1  \\\\\n",
      "... & 1 \\\\\n",
      "x_n & 1  \\end{array} \\Bigg]$\n",
      "$\\bigg[ \\begin{array}{c}\n",
      "a  \\\\\n",
      "b \\end{array} \\bigg]$\n",
      "$=\\Bigg[ \\begin{array}{c}\n",
      "y_1   \\\\\n",
      "...  \\\\\n",
      "y_n  \\end{array} \\Bigg]$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "With a little bit of calculus, we can rearrange the term in order to obtain the parameter vector $\\pmb a = [a\\;b]^T$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\Rightarrow \\pmb a = (\\pmb X^T \\; \\pmb X)^{-1} \\pmb X^T \\; \\pmb y$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "The more classic approach to obtain the slope parameter $a$ and y-axis intercept $b$ would be:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$a = \\frac{S_{x,y}}{\\sigma_{x}^{2}}\\quad$  (slope)\n",
      "\n",
      "\n",
      "$b = \\bar{y} - a\\bar{x}\\quad$ (y-axis intercept)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "where \n",
      "\n",
      "\n",
      "$S_{xy} = \\sum_{i=1}^{n} (x_i - \\bar{x})(y_i - \\bar{y})\\quad$ (covariance)\n",
      "\n",
      "\n",
      "$\\sigma{_x}^{2} = \\sum_{i=1}^{n} (x_i - \\bar{x})^2\\quad$ (variance)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a name=\"implementations\"></a>\n",
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Least squares fit implementations"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[[back to top](#Sections)]"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a name='matrix_approach'></a>\n",
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "The matrix approach in Python and NumPy"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[[back to top](#Sections)]"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "First, let us implement the equation:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\pmb a = (\\pmb X^T \\; \\pmb X)^{-1} \\pmb X^T \\; \\pmb y$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "which I will refer to as the \"matrix approach\"."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Matrix approach implemented in NumPy and (C)Python"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "\n",
      "def matrix_lstsqr(x, y):\n",
      "    \"\"\" Computes the least-squares solution to a linear matrix equation. \"\"\"\n",
      "    X = np.vstack([x, np.ones(len(x))]).T\n",
      "    return (np.linalg.inv(X.T.dot(X)).dot(X.T)).dot(y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a name='classic_approach'></a>\n",
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "The classic approach in Python"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[[back to top](#Sections)]"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next, we will calculate the parameters separately, using standard library functions in Python only, which I will call the \"classic approach\"."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$a = \\frac{S_{x,y}}{\\sigma_{x}^{2}}\\quad$  (slope)\n",
      "\n",
      "\n",
      "$b = \\bar{y} - a\\bar{x}\\quad$ (y-axis intercept)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note: I refrained from using list comprehensions and convenience functions such as `zip()` in\n",
      "order to maximize the performance for the Cython compilation into C code in the later sections.\n",
      "    "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Implemented in (C)Python"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def classic_lstsqr(x_list, y_list):\n",
      "    \"\"\" Computes the least-squares solution to a linear matrix equation. \"\"\"\n",
      "    N = len(x_list)\n",
      "    x_avg = sum(x_list)/N\n",
      "    y_avg = sum(y_list)/N\n",
      "    var_x, cov_xy = 0, 0\n",
      "    for x,y in zip(x_list, y_list):\n",
      "        temp = x - x_avg\n",
      "        var_x += temp**2\n",
      "        cov_xy += temp * (y - y_avg)\n",
      "    slope = cov_xy / var_x\n",
      "    y_interc = y_avg - slope*x_avg\n",
      "    return (slope, y_interc)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a name='sample_data'></a>\n",
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Visualization"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[[back to top](#Sections)]"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To check how our dataset is distributed, and how the least squares regression line looks like, we will plot the results in a scatter plot.  \n",
      "Note that we are only using our \"matrix approach\" to visualize the results - for simplicity. We expect both approaches to produce similar results, which we confirm with the code snippet below."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import random\n",
      "import numpy as np\n",
      "\n",
      "random.seed(12345)\n",
      "\n",
      "x = [x_i*random.randrange(8,12)/10 for x_i in range(500)]\n",
      "y = [y_i*random.randrange(8,12)/10 for y_i in range(100,600)]\n",
      "\n",
      "np.testing.assert_almost_equal(\n",
      "    classic_lstsqr(x, y), matrix_lstsqr(x, y), decimal=5)  \n",
      "    \n",
      "print('ok')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "ok\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from matplotlib import pyplot as plt\n",
      "import random\n",
      "\n",
      "random.seed(12345)\n",
      "\n",
      "x = [x_i*random.randrange(8,12)/10 for x_i in range(500)]\n",
      "y = [y_i*random.randrange(8,12)/10 for y_i in range(100,600)]\n",
      "\n",
      "slope, intercept = matrix_lstsqr(x, y)\n",
      "\n",
      "line_x = [round(min(x)) - 1, round(max(x)) + 1]\n",
      "line_y = [slope*x_i + intercept for x_i in line_x]\n",
      "\n",
      "plt.figure(figsize=(8,8))\n",
      "plt.scatter(x,y)\n",
      "plt.plot(line_x, line_y, color='red', lw='2')\n",
      "\n",
      "plt.ylabel('y')\n",
      "plt.xlabel('x')\n",
      "plt.title('Linear regression via least squares fit')\n",
      "\n",
      "ftext = 'y = ax + b = {:.3f} + {:.3f}x'\\\n",
      "        .format(slope, intercept)\n",
      "plt.figtext(.15,.8, ftext, fontsize=11, ha='left')\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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l74wWGRlJmTJlsixjzJgxjBkzBtBd0q74tMeqhYUFzs7OALi4uNCnTx+OHDmi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\nESNex9Sp5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44dQ7NmbWAy1QQwG8BiAFuh0ZyFQuEJtdoXg9LCMAOjAABfaDzRdswYVN63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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1064c6278>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a name='performance1'></a>\n",
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Performance growth rates"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[[back to top](#Sections)]"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now, finally let us take a look at the effect of different sample sizes on the relative performances for each approach."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import timeit\n",
      "import random\n",
      "random.seed(12345)\n",
      "\n",
      "funcs =  ['classic_lstsqr', 'matrix_lstsqr']\n",
      "\n",
      "orders_n = [10**n for n in range(1,5)]\n",
      "timings = {f:[] for f in funcs}\n",
      "\n",
      "for n in orders_n:\n",
      "    x_list = ([x_i*np.random.randint(8,12)/10 for x_i in range(n)])\n",
      "    y_list = ([y_i*np.random.randint(10,14)/10 for y_i in range(n)])\n",
      "    x_ary = np.asarray(x_list)\n",
      "    y_ary = np.asarray(y_list)\n",
      "    timings['classic_lstsqr'].append(min(timeit.Timer('classic_lstsqr(x_list, y_list)', \n",
      "            'from __main__ import classic_lstsqr, x_list, y_list')\\\n",
      "                                         .repeat(repeat=3, number=1000)))\n",
      "    timings['matrix_lstsqr'].append(min(timeit.Timer('matrix_lstsqr(x_ary, y_ary)', \n",
      "            'from __main__ import matrix_lstsqr, x_ary, y_ary')\\\n",
      "                                         .repeat(repeat=3, number=1000)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import platform\n",
      "import multiprocessing\n",
      "\n",
      "def print_sysinfo():\n",
      "    \n",
      "    print('\\nPython version  :', platform.python_version())\n",
      "    print('compiler        :', platform.python_compiler())\n",
      "    print('NumPy version   :', np.__version__)\n",
      "    \n",
      "    print('\\nsystem     :', platform.system())\n",
      "    print('release    :', platform.release())\n",
      "    print('machine    :', platform.machine())\n",
      "    print('processor  :', platform.processor())\n",
      "    print('CPU count  :', multiprocessing.cpu_count())\n",
      "    print('interpreter:', platform.architecture()[0])\n",
      "    print('\\n\\n')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt\n",
      "\n",
      "def plot(timings, title, labels, orders_n):\n",
      "    plt.rcParams.update({'font.size': 12})\n",
      "\n",
      "    fig = plt.figure(figsize=(11,10))\n",
      "    for lb in labels:\n",
      "        plt.plot(orders_n, timings[lb], alpha=0.5, label=labels[lb], \n",
      "                 marker='o', lw=3)\n",
      "    plt.xlabel('sample size n')\n",
      "    plt.ylabel('time per computation in milliseconds')\n",
      "    #plt.xlim([min(orders_n) / 10, max(orders_n)* 10])\n",
      "    plt.legend(loc=2)\n",
      "    plt.grid()\n",
      "    plt.xscale('log')\n",
      "    plt.yscale('log')\n",
      "    plt.title(title)\n",
      "    plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Results"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[[back to top](#Sections)]"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "title = 'Performance of Linear Regression Least Squares Fits'\n",
      "\n",
      "labels = {'classic_lstsqr': '\"classic\" least squares in (C)Python',\n",
      "          'matrix_lstsqr': '\"matrix\" least squares in in (C)Python + NumPy',\n",
      "         }\n",
      "\n",
      "print_sysinfo()\n",
      "plot(timings, title, labels, orders_n)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Python version  : 3.4.0\n",
        "compiler        : GCC 4.2.1 (Apple Inc. build 5577)\n",
        "NumPy version   : 1.8.1\n",
        "\n",
        "system     : Darwin\n",
        "release    : 13.2.0\n",
        "machine    : x86_64\n",
        "processor  : i386\n",
        "CPU count  : 4\n",
        "interpreter: 64bit\n",
        "\n",
        "\n",
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ITU3FP//8gw4dOgAA/P398f3338Pa2hppaWlIS0uTBPGvmzt3LjZu3Ig1a9Yg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\nb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       "text": [
        "<matplotlib.figure.Figure at 0x103139438>"
       ]
      }
     ],
     "prompt_number": 26
    }
   ],
   "metadata": {}
  }
 ]
}